Geological log data processing methods and apparatuses

ABSTRACT

A method and a resistivity image logging tool connected or connectable to one or more processing devices process geological log data to construct missing information from destroyed or occluded parts using cues from observed data. The geological log data signals can be generated through use of the logging tool having one or more electrodes interacting with a formation intersected by a borehole. The processing involves the steps of: in respect of one or more data dimensions associated with missing values in a log data set, decomposing the signal into a plurality of morphological components; and morphologically reconstructing the signal such that missing values are estimated.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a divisional of U.S. application Ser. No. 13/789,374, filed 7Mar. 2013, which is incorporated herein by reference and which claimspriority under 35 U.S.C. § 119 to UK Appl. No. GB1210533.4, filed on 14Jun. 2012, and UK Appl. No. GB1300933.7, filed on 18 Jan. 2013, thecontents of each one incorporated herein by reference.

FIELD OF THE DISCLOSURE

The invention relates to geological log data processing methods andapparatuses. In particular the method and apparatus of the invention areuseful for reconstructing missing or incomplete data in a region of asubterranean borehole that has undergone a logging process.

BACKGROUND OF THE DISCLOSURE

A geological formation may be penetrated by a borehole for the purposeof assessing the nature of, or extracting, a commodity of commercialvalue that is contained in some way in the formation. Examples of suchcommodities include but are not limited to oils, flammable gases,tar/tar sands, various minerals, coal or other solid fuels, and water.

When considering the assessment and/or extraction of such materials thelogging of geological formations is, as is well known, economically anextremely important activity.

Virtually all commodities used by mankind are either farmed on the onehand or are mined or otherwise extracted from the ground on the other,with the extraction of materials from the ground providing by far thegreater proportion of the goods used by humans.

It is extremely important for an entity wishing to extract materialsfrom beneath the ground to have as good an understanding as possible ofthe conditions prevailing in a region from which extraction is to takeplace.

This is desirable partly so that an assessment can be made of thequantity and quality, and hence the value, of the materials in question;and also because it is important to know whether the extraction of suchmaterials is likely to be problematic.

The acquisition of such data typically makes use of techniques of wellor borehole logging. Logging techniques are employed throughout variousmining industries, and also in particular in the oil and gas industries.The invention is of benefit in well and borehole logging activitiespotentially in all kinds of mining and especially in the logging ofreserves of oil and gas.

In the logging of oil and gas fields (or indeed geological formationscontaining other fluids) specific problems can arise. Broadly statedthis is because it is necessary to consider a geological formation thattypically is porous and that may contain a hydrocarbon-containing fluidsuch as oil or natural gas or (commonly) a mixture of fluids only onecomponent of which is of commercial value.

This leads to various complications associated with determining physicaland chemical attributes of the oil or gas field in question. Inconsequence a wide variety of well logging methods has been developedover the years. The logging techniques exploit physical and chemicalproperties of a formation usually through the use of a logging tool orsonde that is lowered into a borehole (that typically is, but need notbe, a wellbore) formed in the formation by drilling.

Broadly, in most cases the tool sends energy into the formation anddetects the energy returned to it that has been altered in some way bythe formation. The nature of any such alteration can be processed intoelectrical signals that are then used to generate logs (i.e. graphicalor tabular representations containing much data about the formation inquestion) and, in the case of some logging tool types, images thatrepresent conditions and substances in downhole locations.

An example of a logging tool type is the so-called multi-padmicro-resistivity borehole imaging tool, such as the tool 10 illustratedin transversely sectioned view in FIG. 1. In this logging tool anannular array of (in the example illustrated) eight pads 11 each in turnsupporting typically two lines of surface-mounted resistivity electrodesreferred to as “buttons” 12 is supported on a series of calliper arms 13emanating from a central cylinder 14. During use of the tool 10 the arms13 press the buttons 12 into contact with the very approximatelycylindrical wall of a borehole. The borehole is normally filled with afluid (such as a water-based mud) that if conductive provides anelectrical conduction path from the formation surrounding the boreholeto the buttons.

Many variants on the basic imaging tool design shown are known. In somemore or fewer of the pads 11 may be present. The numbers and patterns ofthe buttons 12 may vary and the support arms also may be of differingdesigns in order to achieve particular performance effects. Sometimesthe designers of the tools aim to create e.g. two parallel rows ofbuttons located on the pad one above the other. The buttons in the lowerrow are offset slightly to one side relative to their counterparts inthe row above. When as described below the signals generated by thebuttons are processed the outputs of the two rows of buttons are ineffect lain over one another. As a result the circumferential portion ofthe borehole over which the buttons 12 of a pad 11 extend is logged asthough there exists a single, continuous, elongate electrode extendingover the length in question.

In general in operation of a tool such as resistivity tool 10 electricalcurrent generated by electronic components contained within the cylinder14 spreads into the rock and passes through it before returning to thepads 11. The returning current induces electrical signals in the buttons12.

Changes in the current after passing through the rock may be used togenerate measures of the resistivity or conductivity of the rock. Theresistivity data may be processed according to known techniques in orderto create (typically coloured) image logs that reflect the make-up ofthe rock and any minerals or fluids in it. These image logs convey muchdata to geologists and others having the task of visually inspecting andcomputationally analysing them in order to obtain information about thesubterranean formations.

In use of a tool such as that shown in FIG. 1 the tool is initiallyconveyed to a chosen depth in the borehole before logging operationscommence. The deployed location may be many thousands or tens ofthousands of feet typically but not necessarily below, and in any eventseparated by the rock of the formation from, a surface location at whichthe borehole terminates.

Various means for deploying the tools are well known in the mining andoil and gas industries. One characteristic of most if not all of them isthat they can cause a logging tool that has been deployed as aforesaidto be drawn from the deployed location deep in the borehole back towardsthe surface location. During such movement of the tool it logs theformation, usually continuously. As a result the image logs may extendcontinuously for great distances.

Although the logs are continuous in the longitudinal sense,notwithstanding the pad offsetting explained above they are azimuthallyinterrupted by reason of the pads not extending all the way continuouslyaround the circumference of the borehole. The design of the toolprevents this since the arms 13 must be extensible in order to press thepads 11 into contact with the borehole wall. Following extension of thearms there exists a series of gaps between the ends of the pads.

No data can be logged in these gaps, which manifest themselves aselongate spaces in the image logs. An example of an image log 16including several of these gaps or discontinuities 17 is visible in FIG.2. The discontinuities extend from one end of the reconstructed imagelog to the other, a distance in some cases of thousands of feet.

Filling in the missing data is advantageous for obvious reasons of thedesirability of completeness of information. Moreover it is likely to berequired when it is desired to process the image logs using automaticpattern recognition programs in order to try and identify certainfeatures in the logs.

SUMMARY OF THE DISCLOSURE

An aim of the invention is to produce dependable, continuous resistivityimage logs notwithstanding the inability to log the gap regions.

The invention furthermore is suitable to make allowances for incompletelogging in a range of other types of log that may be produced forexample with tools of types other than the exemplary, non-limitingresistivity tool described herein. A non-exhaustive list of applicationsof the invention includes: making up for missing data in a wide range ofmeasurement systems used in open-hole situations and in which one ormore sensors fails during logging; processing of log data from casedhole situations in which it is required to image the inside or theoutside of the casing for the purpose of assessing its integrity or forsimilar reasons; creating other array measurement logs and signals thatmay or may not be rendered as images.

Examples of cased hole imaging measurements, to which the invention isapplicable, include magnetic flux leakage measurements, ultrasonicscanning measurements and multi-fingered calliper measurements each ofwhich will be known to the worker of skill in the art.

It has previously been proposed to try and make up for discontinuitiesof the kind described through the use of a 1D interpolation conceptinvolving taking the rows of the image and applying cubic interpolationbetween the 1D data to restore the missed value at each interrupted datapoint. The process is applied to the whole image by scrolling downthrough rows. However, the results have been found to be very basic andnot all the missed details are recovered.

Testing this approach on real data may give quickly generated answersbut these tend to be far from perfect. The 1D interpolation technique isbelieved to fail in the homogenous image parts where straight verticallines are visible. This issue can cause a problem when dealing withpattern recognition and edge detection, for example, since thesevertical lines can appear as false edge detections.

For these reasons the inventors have rejected the 1D interpolationtechnique in favour of the methods and apparatuses defined and describedherein.

Patent application no GB 1210533.4, from which this application claimspriority, describes a technique of morphological component analysis(MCA) that is highly effective in reconstructing missing or occludeddata in log data sets in general, and image log data in particular.

The inventors however have identified that improvements in thetechniques described in application no GB 1210533.4 are possible anddesirable.

Such improvements fall into two main categories:

-   -   pre-processing of image log data in order to improve its        suitability to undergo MCA processing, or other processing        intended to make up for lost, missing or occluded data; and    -   selection of the precise data generation technique that is most        appropriate to the character of the log data and the processing        capacity available.

In a first aspect according to the invention there is provided a methodof preparing geological log data for processing to construct missinginformation from destroyed or occluded parts, the method comprising oneor more of the steps of:

-   a. identifying and taking account of one or more null values in the    log data;-   b. compensating for at least one variation in one or more    environmental factors that are variable depending on the environment    to which the log data pertain;-   c. normalising data within specific areas of the log data; and-   d. normalising data between specific areas of the log data.

The inventors have found that the foregoing steps are desirable andhelpful pre-processing steps that usefully condition the log data fortreatment according to an MCA or other data re-creation technique.

Preferably the step a. of identifying and compensating for one or morenull and/or outlying values (herein “null” values) in the log dataincludes a1. identifying one or more elements of the log data thatexhibit a null value characteristic; a2. assessing whether each saidelement is relatively isolated in the elements of the log data or isrelatively unseparated from other elements exhibiting a null valuecharacteristic, the relative isolation being determined with referenceto a predetermined measure of relative isolation; and a3. if a saidelement is relatively isolated, excluding it from further consideration.

This optional aspect of the method of the invention permits anysubsequently performed steps of making up for missing data to avoidseeking to process the log data in areas that do not correspond tomissing data of the general kinds described herein.

As a further, optional pre-processing step the step b. of the method, ofcompensating for the variation in sensitivity across the button arrayfrom one end of a pad of a resistivity logging tool to the othercompensates for at least one variation in one or more environmentalfactors that are variable depending on the environment to which the logdata pertain.

The inventors have found that the response of e.g. a pad of aresistivity image logging tool to environmental factors varies dependingon the part of the pad under consideration. This is partly because eachbutton electrode within a pad is sensitive to the resistivity of itssurroundings to a slightly differing degree by virtue of the uniquegeometrical position of each button within a pad, which gives rise tosystematic variations in current flow across the button arrays. It isalso partly because the curvature of the pad almost never matchesexactly the curvature of the part of the borehole wall against which itis pressed by the calliper arms, with the result that the spacings ofindividual pads from the material of the formation is not constant fromone end of the pad to the other. This in turn may mean that more or lessborehole fluid for example is interposed between the pads and theborehole wall, depending on the part of the pad under consideration.

However further factors are believed also potentially to be relevant tothe sensitivity of the tool to environmental factors. In consequenceoptionally the step b. of compensating for at least one variation in oneor more environmental factors that are variable depending on theenvironment to which the log data pertain includes compensating one ormore elements of the log data for one or more variations selected fromthe following list including:

-   i. the standoff between the pads of the logging tool and the    formation and/or-   ii. variations in mudcake thickness and/or-   iii. variations in mudcake constitution.

The inventors advantageously have found that the foregoing parameterscan noticeably influence the environmental sensitivity of the loggingtool.

Preferably the step c. of normalising data within specific areas of thelog data includes calculating and applying an environmental correctionfactor, for each resistivity value derived from the log data,corresponding to a respective pad strip of a resistivity logging tool.

The inventors have found that this pre-processing step is useful andhelpful in terms of improving the quality of log data reconstructedusing the remainder of the method steps of the invention.

More preferably each said resistivity value is represented as a pixel inan image derived from the log data.

Even more preferably Step c defined above includes the sub-steps of:

-   c1. based on the number of resistivity values in a set of said log    data corresponding to a respective line of pads, approximately    determining the positions, in the said set of log data, of    respective buttons of a said pad strip;-   c2. determining the median value of resistivity of a centre    resistivity value, of the said set of log data, determined with    respect to a predetermined sliding depth window; and-   c3. normalizing the other resistivity values of the set of log data    to that of the centre resistivity value.

This sequence of method steps advantageously assists in reducing theeffects of variations in the sensitivity to environmental factors thatare apparent when comparing buttons in different parts of a pad, assummarised above.

The method of the invention also preferably includes defining a strip ofresistivity values corresponding to a respective pad of a resistivitylogging tool defining a window centred on a log depth measurementpertinent to the strip of resistivity values and for each line in thesaid window as necessary re-sampling the strip so that the number ofresistivity values corresponds to the number of buttons in the padbefore calculating the mean resistivity of the line; for each re-sampledcolumn of resistivity values in the window, calculating the median ofthe pixel value for each line divided by the corresponding line mean;for each resistivity value in the line in question, dividing theresistivity value by the resulting column median; re-sampling the lineto an initial resolution; repeating the foregoing steps for the nextline and, when all the lines in a said strip have been so processed,repeating the steps in respect of a further said strip.

The inventors have found that the foregoing steps advantageously improvethe uniformity of the image within pad strips compared with the priorart. Such steps may be repeated for one or more further values of logdepth, until all the strips in a plurality of pads have beenpre-processed in this fashion.

As a further part of the process of taking account of variations in theresponses of different parts of a logging tool to environmental factorsstep d of the method of the invention, of normalising data betweenspecific areas of the log data, includes calculating the average of aresistivity value for each pad of a multiple pad-derived resistivitylog; and normalising the average resistivity values to a commonresistivity value whereby to account for any differential sensitivity ofrespective said pads to conditions in the locations at which log dataare acquired.

The use of normalised log data is made possible by the preceding steps,set out above, relating to compensating for variations in environmentalsensitivity.

Conveniently the method includes the step of determining whether animage constructed based on the data includes more than a thresholdproportion of sub-parallel sinusoids. If so the method then preferablyincludes performing a fast 2D correlation in order to construct missinginformation from destroyed or occluded parts of the image.

An advantage of selecting a 2D correlation approach to filling inmissing data in the event of the number of sub-parallel sinusoids in animage under study exceeding a threshold number relates to the amount ofprocessing capacity required to perform the steps of the method of theinvention, described below, relating to Morphological Component Analysis(MCA).

MCA is computationally demanding to carry out. If therefore the image issuitable for treatment by another, computationally simpler, method thisis performed in order to minimise processing time and requirements. Thetest of suitability in this regard identified by the inventors is thatof the number of sub-parallel sinusoids, which in turn indicates thesuitability of the image for processing by way of a 2D correlationtechnique in order to fill in missing or occluded data.

The 2D correlation method while less accurate than the MCA techniquedescribed herein is nonetheless an acceptable technique under somecircumstances.

When however the 2D correlation method is in accordance with the testindicated above regarded as not suitable for the image log data inquestion, in accordance with a second aspect of the invention a methodof processing geological log data to construct missing information fromdestroyed or occluded parts using cues from observed data comprises thesteps of:

-   e. in respect of one or more data dimensions associated with missing    values in a log data set, decomposing the signal into a plurality of    morphological components and-   f. morphologically reconstructing the signal such that missing    values are estimated.

Preferably the method includes performing Steps e. and f. in respect ofall the missing information in the data set.

Also preferably the morphological components include texture andpiece-wise parts.

The approach of the method of the invention to filling in the missingdata involves adopting a 2D concept and approaching the problem as aninverse one, in which it is necessary to de-convolve the targeted imagefrom the observed (measured) one, which is basically the image convolvedwith a mask (the missing data). To do this it is necessary to introducethe MCA of an image. Successful MCA methods have many far-reachingapplications in science and technology.

Because MCA is related to solving underdetermined systems of equationsit might also be considered, by some, to be problematic or evenintractable. The major problem involves decomposing a signal or imageinto superposed contributions from different sources assuming theoverall signal or image was built by layered information. For example,an n-pixel image created by superposing K different types offers us ndata (the pixel values) but there may be as many as n×K unknowns (thecontribution of each content type to each pixel).

Relying on linear algebra, it is not recommended to attempt thedecomposition and morphological reconstruction steps of the method ofthe invention as there are more unknowns than equations. On the otherhand, if prior information is known about the underlying object, thereare some rigorous results showing that such separation can be possible.

To this end the decomposition in a sparse representation includes use ofa dictionary of elemental bases including one or more selected from thelist including discrete cosine transforms (DCT), wavelet transforms,wavelet packet transforms, ridgelet transforms, curvelet transforms, andcontourlet transforms.

Preferably the method of the invention includes the step of performingone or more automatic feature recognition and/or machine interpretationsteps following Step f.

Further preferably at least one said automatic feature recognitionand/or machine interpretation step includes one or more of an edgerecognition step and/or a texture recognition step.

In more detail the method of the invention preferably includes the Stepg. of separating each elemental signal base into a plurality ofrespective morphological components on the basis of an assumption thatin order for each elemental signal behaviour base to be separated thereexists a dictionary of elemental bases enabling its construction using asparse representation.

Further preferably the method includes the Step h. of assuming that eachrespective morphological component is sparsely represented in a specifictransform domain; and the Step i. of amalgamating each transformattached to a respective morphological component into a dictionary. Thedictionaries referred to herein may thus advantageously be formed fromthe data of the signals undergoing processing in accordance with themethod of the invention.

The method may in such a case advantageously and efficiently theninclude the Step j. of identifying the sparsest representation ofmorphological components and using the thus-identified components tode-couple the components of the signal content. The inventionfurthermore optionally may include the use of a pursuit algorithm tocarry out Step j.

Basis pursuit (BP) is a principle for decomposing a signal into an“optimal” superposition of dictionary elements, where optimal meanshaving the smallest l1 norm of coefficients among all suchdecompositions.

The method of the invention fills in missing data considerably moreaccurately than the prior art 1D method described above. The inventorshave found that this increased accuracy made apparent the variations,described above, in the environmental sensitivity factor of each buttonof a resistivity imaging tool, this relating to the transformation ofmeasured resistance at a button to the required resistivity, andcomprising parts related to the geometry of the tool and parts relatingto the environment in which the tool operates.

Conveniently in preferred embodiments of the invention the piece-wiseparts are or include image content; the Step e. includes separating thetexture parts and image content; and the method includes separatelyconstructing information missing from the texture parts and imagecontent, before performing Step f.

The inventors have found this approach to be computationally achievablein an acceptable time period.

Preferably the geological log data are measures of formation resistivityin the form of an image containing N pixels; and further preferably themethod includes representing the geological log data as aone-dimensional vector, of length N, by lexicographic ordering.

In more detail preferably the method of the invention includes the Stepe1. of representing the image content by a dictionary:A_(n) ∈

^(N×L)wherein the basis pursuit algorithm is such the image content issparsely represented in dictionary A_(n).

Furthermore for the avoidance of doubt preferably sparsity as usedherein is quantified by one of a plurality of quasi-norms.

Preferably the quasi-norm is the l₀ norm, which is equivalent to thenumber of non-zero components in the vector x and l_(p)-norms∥x∥_(p)=(Σ|x(i)|^(p))^(1/p) with p<1, and in which small values of anyof these indicate sparsity. However other quasi-norms may be suitablefor use in the method of the invention, as further described below.

When the quasi-norm is the l₀ norm, preferably the pursuit algorithmseeks to solve:

$\left\{ {\underset{\_}{x}}_{n}^{opt} \right\} = {{\underset{\{{\underset{\_}{x}}_{n}\}}{argmin}{{\underset{\_}{x}}_{n}}_{0}\mspace{14mu}{s.t.\mspace{14mu}\underset{\_}{Y}}} = {A_{n}{\underset{\_}{x}}_{n}}}$with the result that A_(n) x _(n) contains the image content.

Again, the preferred approach therefore advantageously seeks to treatthe image content parts separately. This is believed to be a majorcontributor to the ability of the method of the invention successfullyto perform MCA on image log data.

In another embodiment of the method of the invention, the quasi-norm isthe l₁, norm, and the pursuit algorithm seeks to solve

$\left\{ {\underset{\_}{x}}_{n}^{opt} \right\} = {{\underset{\{{\underset{\_}{x}}_{n}\}}{argmin}{{\underset{\_}{x}}_{n}}_{1}\mspace{14mu}{s.t.\mspace{14mu}\underset{\_}{Y}}} = {A_{n}{\underset{\_}{x}}_{n}}}$with the result that A_(n) x _(n) contains the image content.

In such a case, the pursuit algorithm preferably is a basis pursuit (BP)that solves the expression using linear programming.

In more detail, preferably the pursuit algorithm seeks to solve:

$\left\{ {\underset{\_}{x}}_{n}^{opt} \right\} = {{\underset{\{{\underset{\_}{x}}_{n}\}}{argmin}{{\underset{\_}{x}}_{n}}_{1}\mspace{14mu}{s.t.\mspace{11mu}{\;{\underset{\_}{Y} - {A_{n}{\underset{\_}{x}}_{n}}}}_{2}}} < ɛ}$in which ε is a parameter corresponding to the level of noise in theimage log Y, with the result that A_(n) x _(n) contains the imagecontent.

Alternatively, the pursuit algorithm may seek to solve:

$\left\{ {\underset{\_}{x}}_{n}^{opt} \right\} = {{\underset{\{{\underset{\_}{x}}_{n,}\}}{argmin}{{\underset{\_}{x}}_{n}}_{1}} + {\lambda{\;{\underset{\_}{Y} - {A_{n}{\underset{\_}{x}}_{n}}}}_{2}^{2}} + {\gamma\;{TV}\left\{ {A_{n}{\underset{\_}{x}}_{n}} \right\}}}$in which TV represents a total variation penalty and the parameter λ>0is a scalar representation parameter and the total variation penaltyincreases the sparseness gradient of A_(n) x _(n), with the result thatA_(n) x _(n) contains the image content.

Conveniently, the Step f. may include assuming that pixels, of an imagelog, corresponding to missing log data are indicated by a mask matrix M∈

^(N×L) the main diagonal M of which encodes the pixel status as 1 in thecase of an existing pixel and 0 is the case of missing data and whereinthe pursuit algorithm seeks to solve:

$\left\{ {\underset{\_}{x}}_{n}^{opt} \right\} = {{\underset{\{{\underset{\_}{x}}_{n}\}}{argmin}{{\underset{\_}{x}}_{n}}_{1}} + {\lambda{\;{\underset{\_}{M\left( Y \right.} - {A_{n}{\underset{\_}{x}}_{n}}}}_{2}^{2}} + {\gamma\;{TV}\left\{ {A_{n}{\underset{\_}{x}}_{n}} \right\}}}$with the result that A_(n) x _(n) contains the image content.

For the avoidance of doubt, the method of the invention includes withinits scope a method of processing geological log data including carryingout the steps of Paragraph [0030] hereof followed by the steps of atleast Paragraph [0051] hereof.

The invention also resides in a resistivity image logging tool havingoperatively connected or connectable thereto one or more processingdevices for carrying out on data signals generated by the tool a methodas defined herein.

Furthermore, in accordance with the invention, there is provided aprogrammable processing device that is programmed to carry out a methodas defined herein.

In yet a further aspect of the invention, there is provided dataprocessed in accordance with a method as defined herein.

BRIEF DESCRIPTION OF THE DRAWINGS

There now follows a description of preferred embodiments of theinvention, by way of non-limiting example, with reference being made tothe accompanying drawings in which:

FIG. 1 is a transversely sectioned view of an eight-buttonmicro-resistivity imaging tool;

FIG. 2 is an example of an image log that has been created from theoutput of a resistivity logging tool such as that of FIG. 1, in whichthe elongate data gaps are starkly apparent as coherent lines extendingalong the length of the image and to which the method of the inventionbeneficially is applicable;

FIG. 3 is an example of another image log exhibiting the missing dataphenomenon as a result of the pad and arm design of the resistivityimaging tool used to acquire the log data, and to which the method ofthe invention beneficially is applicable;

FIG. 4 is a flow-chart showing steps in the method of the invention,including pre-processing steps as defined herein and (in summary form)post-MCA visualisation steps that are related to the method of theinvention;

FIG. 5 is an image of a graphical user interface generated in aprogrammable device according to the invention and representing theoutput of the method steps of the invention;

FIG. 6 shows an image log that is similar to those of FIGS. 2 and 3 andto which the method of the invention has been successfully applied inorder to make up for missing data in the coherent bands visible in FIGS.2 and 3;

FIGS. 7a to 7c are a comparison between an originally generated imagelog (FIG. 7a ) including the bands of missing data, an attempt atfilling in the missing data using a prior art 1D interpolation technique(FIG. 7b ) and the method of the invention (FIG. 7c );

FIGS. 8a to 8c are similar comparisons in which a need for environmentalsensitivity adjustment in conjunction with the method of the invention,caused by the greater accuracy of the method of the invention than theprior art methods, is apparent;

FIGS. 9a and 9b illustrate the dimensional aspects of a typicalresistivity imaging tool pad that give rise to the environmentalsensitivity considerations mentioned, 9 a being a cross-section showingthe pad curvature and 9 b being indicative of the distribution of buttonelectrodes on the face of the pad;

FIG. 10 is a flowchart summarising one practical implementation of themethod of the invention, and hence showing the stage “Apply MCAIn-painting” of the flowchart of FIG. 4 in more detail; and

FIGS. 11a to 11b illustrate a phenomenon of residual differences betweenpads that in some cases also must be taken account of in processing ofimage log data in accordance with the invention.

DETAILED DESCRIPTION OF THE DISCLOSURE

As explained hereinabove, the use of e.g. a multi-pad micro-resistivitytool, or any of a number of other logging tool types, can lead todiscontinuities in the data used to assemble image logs. Also asexplained, these discontinuities manifest themselves as coherent bandsor lines 17 as shown in FIGS. 2 and 3 that are empty of data.

FIG. 2 illustrates the kinds of data void that arise through use of aknown imaging tool having an outer diameter in use (i.e. when themoveable calliper arms are deployed) of 4.2 inches. In one known form ofsuch a tool each pad 11 supports two parallel rows of twelve buttons 12.The rows are offset as described above. This arrangement gives rise tothe comparatively narrow, but still significantly inconvenient, bands 17of no data in the image log.

FIG. 3 shows the much broader voids that arise through use of aresistivity tool having an outer diameter in use of 2.4 inches.

One form of tool of this size has pads 11 each supporting two parallel,offset rows of four buttons 12. The gaps between the ends of the sets ofoffset rows are greater as a result of the smaller size of and greaterspacing between the pads so the data void bands 17 are significantlywider than in FIG. 2.

Patent application no GB 1210533.4 describes an MCA In-Painting methodthe effect of which is to fill in the missing data in image logs such asthose of FIGS. 2 and 3, in a manner that is consistent with theremainder of the data in the log and that allows subsequent processingand interpretation of the resulting whole image. The inventors howeveras stated have realised that a certain amount of pre-processing of theimage log data is desirable in order to render the MCA In-Paintingtechnique as successful as possible.

FIG. 4 summarises the steps through which the pre-processing actionsintegrate with the steps of the MCA technique defined herein.

As represented by Step S1, the method of the invention involvesinitially importing a speed-corrected, oriented image from a log dataacquisition program. The steps of the invention however are equallyapplicable to log data provided in the formats supported by numerousother log data conveying applications.

At Steps S2 and S3, the logic of the method of the invention includesone or more of the steps of:

-   a. identifying and taking account of one or more null values in the    log data;-   b. compensating for at least one variation in one or more    environmental factors that are variable depending on the environment    to which the log data pertain;-   c. normalising data within specific areas of the log data; and-   d. normalising data between specific areas of the log data, with    Steps a., b., c. and d. optionally including further detailed    aspects as set out in Paragraphs [0031] through [0050] hereof.

Such steps involve:

Dropout Removal

This routine removes null values that occasionally exist within pad dataand replaces them with values interpolated from neighbouring points.

Data Driven Environmental Normalisations

It is known that the homogeneous environment sensitivity of each buttonvaries systematically by across the pads. Additional to the sensitivityvariation, the effect of standoff/mudcake causes a further systematicvariation, this being substantially larger. It is more apparent onun-normalized inpainted images because of the lever effect associatedwith the pad edges. Moreover the variations are typically more complexand less smooth than obtained from models (which represent ideal cases).For this reason—and also because models cover only a sub-set ofenvironments—it is necessary to derive the environmental normalizationsfrom the data itself, taking account of the fact that the data is asuperposition of information from the borehole and formation.

Within—Pad Normalization

This algorithm calculates and applies an environmental correction factorfor each pixel within each pad. It would be preferable to perform thenormalization on button data, but if the link to buttons is lost aftercreation of an image it will be necessary to work with pixels. Knowingthe number of pixels across each pad stripe allows the method to inferbutton locations; taking the average resistivity of the centre pixelover a defined sliding depth window (excluding values likely to beassociated with formation boundaries), the algorithm normalizes allother pixels on the pad to the central value.

The first step is the removal of all pixels with value −999.75 (or someother arbitrary null value used by the log data handling software), thisbeing the value used by one form of data acquisition application torepresent non-measured or null data.

Thereafter, the steps are:

-   A. For each strip of pixels representing a single pad, take a window    centred on the current depth. For each line within the window it is    convenient to re-sample each of the pad strips to the number of    buttons on each pad. This makes it easier to perform the vertical    averaging in step B (below) in cases where the number of pixels per    strip is changing within a window due to changes in borehole size.-   B. For each line in this window:    -   Determine the maximum and minimum value. If the ratio max/min is        less than a threshold then this line is included in the        computation of an average (or median) value for each column from        the lines in the current window. Otherwise, when the ratio        exceeds the threshold, the line is not included in this        calculation.-   C. Apply the normalization to the centre line (by dividing each    pixel by the corresponding column average) regardless of whether the    max/min ratio for this line is below the ratio threshold.-   D. Resample the line back to the original resolution and place it in    the normalized image output.

The calculation is repeated for each depth in the file. Note also thatthe normalization operates on the logarithms of the resistivity values,the algorithm converting back to linear resistivity at the end of theprocess.

After within-pad normalization sometimes there exist residualdifferences between pads, as exemplified by FIGS. 11a and 11 b.

This is due to a differential sensitivity to the environment associatedwith the upper and lower pads, and a second (between pad) normalizationis needed to remove this.

In more detail, FIG. 11a shows borehole effects observed in an imagethat has been the subject of an In-Painting technique such as thatdefined herein. The visual effects apparent in FIG. 11a are the resultof variations in resistivity values that as shown averaged in a depthwindow in FIG. 11b are somewhat pronounced from one pad of theresistivity logging tool to the next.

FIG. 11b shows that after correcting for environmental effects withineach pad, small residual differences exist between the pad averagevalues, the example being from a single geological bed. These residualdifferences are also normalized within the method described herein.

Between—Pad Normalization

This algorithm calculates the average of the within-pad normalizedresistivity values for each pad, and normalizes them to a common valuein order to remove any differential sensitivity between pads.

At Step S4, the method of the invention involves assessing the number ofsub-parallel sinusoids in the thus pre-processed image underconsideration and, depending on whether the number is more or less thana threshold value, selecting (Steps S5 and S6) either processing of theimage data using the MCA In-Painting technique defined herein as part ofthe invention (if the number of sub-parallel sinusoids is below thethreshold); or processing of the image data using a 2D correlationin-painting method.

As stated, the inventors have found that when the number of sub-parallelsinusoids is high the 2D correlation technique is a preferable way offilling in or otherwise taking account of the gaps in the image datacaused by the nature of the image resistivity logging tool as explainedabove.

The reason for this is that when the number of sub-parallel sinusoids isat a high value the processing time and complexity associated with useof the MCA technique become unacceptable. The 2D correlation technique,involving less complex algorithms than the MCA method steps, may becompleted in an acceptable processing cycle time in such circumstances.

If, however, the number of sub-parallel sinusoids is at an acceptablelevel, the MCA processing method steps, as defined herein, arepreferable and therefore are selected at Step S6.

Use of the MCA In-Painting steps of the method of the invention asdefined herein gives rise to the complete image plot 16 visible in FIG.6. As is apparent from the figure the missing data bands are filled inwith very high accuracy and realism.

The image log of FIG. 6 is highly suitable for processing usingautomatic pattern recognition and machine interpretation techniques tothe use of which, broadly, the invention additionally pertains. TheSteps S7-S9 of the flowchart of FIG. 4 summarise some actions that aredesirable in order to prepare the image log for such treatment. Thesevisualisation steps do not form part of the invention as claimed herein.

The output of the steps of FIG. 4 may in accordance with the inventionbe presented in a graphical form as shown in FIG. 5. This illustratesone form (of many possible embodiments) of graphical interface that mayarise in a programmable device, including a display that forms part ofthe apparatus of the invention.

In FIG. 5, Image Pane A shows the whole log data, using a per se knownzoom function that is commonly employed for the purpose of viewingselected parts of image logs; Pane B shows the interrupted image thatresults from use of a resistivity image logging tool; and Panes C and Dshow the image log processed in accordance with steps according to theinvention

Thus, the apparatus of the invention is capable of presenting in-paintedimages in a convenient way that a log analyst or geologist may use whencomparing the un-processed image logs and those treated in accordancewith the method of the invention.

The graphical interface typically would be provided at a surface-locatedcomputer to which the resistivity image logging tool is operativelyconnected or connectable for the purpose of transferring the log data.The interface of FIG. 5 however may in the alternative be provided atanother location, and may indeed if desired be viewed a considerabledistance away from the location at which logging of the borehole takesplace.

FIGS. 7a to 7c as mentioned are a comparison between an originallygenerated image log (FIG. 7a ) including the bands of missing data, anattempt at filling in the missing data using a prior art 1Dinterpolation technique (FIG. 7b ) and the method of the invention (FIG.7c ). As is apparent from FIGS. 7a to 7c although the prior art 1Dinterpolation technique produces some improvement over the untreatedimage log of FIG. 7a the resolution and accuracy of the image are notacceptable. The FIG. 7c image log on the other hand, that has undergonea process comprising the steps of in respect of one or more datadimensions associated with missing values in a log data set, decomposingthe signal into a plurality of morphological components andmorphologically reconstructing the signal such that missing values areestimated, is of superior quality.

FIGS. 8a to 8c are a further comparison of an untreated resistivityimage log (FIG. 8a ), a 1D interpolation treated image log (FIG. 8b )and an image log treated in accordance with the method of the invention,in which a need for environmental sensitivity adjustment, caused by thegreater accuracy of the method of the invention than the prior artmethods, is apparent.

This phenomenon manifests itself as tramlines 18 that result fromvariations in the environmental sensitivity as defined herein from oneside of a pad 12 to the other. Up to now it has been assumed that thevalue of environmental sensitivity is the same for all buttons in anarray supported on a pad, but the method of the invention has revealedthat the value in fact varies in a systematic way across the array. Thisis caused by the constant radius of curvature (that in the exampleillustrated in FIG. 9a is 100 mm) not being the same across the wholewidth of the pad 11 as that of the borehole wall against which it ispressed by the calliper arms supporting it; by the presence of a thinsemi-permeable mudcake that commonly separates the pad from the boreholewall; and by variation in inherent sensitivity associated with theposition of each button within each pad.

FIG. 9b incidentally clearly illustrates a typical lateral offset ofadjacent rows of the buttons 12 in order to try and achieve continuousimaging coverage over the width of the pad 11, with the data voids 17arising chiefly because of the gaps between the ends of the rows ofbuttons 12 shown and those of the next adjacent pads.

The steps of the MCA In-painting technique, assuming this is selected atStep S5 of FIG. 4, may be explained by the following. FIG. 10 summarisessuch method steps in flow chart form.

MCA Method Steps

MCA involves decomposing a signal or image into superposed contributionsfrom different sources assuming it was built by layered information. Inso doing it must solve an underdetermined system of equations—commonlyconsidered to be problematic or even (arguably) intractable.

The fundamental problem is that an N-pixel image created by superposingK different types of morphological components offers N data values (thepixel values) but there may be as many as N×K unknowns (the contributionof each content type to each pixel).

The fact that there are more unknowns than equations makes the problemimpossible to solve using conventional techniques. On the other hand, ifprior information is available about the underlying object, thenaccording to the work of the inventors such separation becomes possibleusing the special techniques described and claimed herein.

Morphologically decomposing a signal into its building blocks is animportant challenge in signal and image processing. Part of this problemtargets decomposition of the image to texture and piece-wise-smooth(cartoon) parts carrying only geometric information. MCA is based on thesparse representation of signals concept. It assumes that each signal isthe linear mixture of several layers, the so-called MorphologicalComponents, that are morphologically distinct, e.g. sines and bumps inthe resistivity images. The success of this method relies on theassumption that—for every atomic signal behaviour to be separated—thereexists a dictionary of atoms that enables its construction using asparse representation. It is then assumed that each morphologicalcomponent is sparsely represented in a specific transform domain.

When all transforms (each one attached to a morphological component) areamalgamated in one dictionary, each one must lead to sparserepresentation over the part of the signal it is serving, while beinghighly inefficient in representing the other content in the mixture. Ifsuch dictionaries are identified, the use of a pursuit algorithmsearching for the sparsest representation leads to the desiredseparation. This is an important aspect of the method of the invention.

MCA is capable of creating atomic sparse representations containing as aby-product a decoupling of the signal content. To exploit the MCAconcept, one may consider the in-painting problem as a missing dataestimation problem (the non-covered zone related to the gaps betweenpads). As explained above, in-painting herein means restoring missingdata information not measured by the pad buttons of the resistivity toolbased upon the measured available (observed) data. In other words,in-painting is an interpolation of the non-measured data due to the gapbetween pads (as exemplified by FIG. 1).

Following recent advances in modern harmonic analysis, many novelrepresentations, including the wavelet transform, curvelet, contourlet,ridegelet, steerable or complex wavelet pyramids, are now known to bevery effective in sparsely representing certain kinds of signals andimages. For decomposition purposes, the dictionary will be built bytaking the union of one or several (sufficiently incoherent) transforms,generally each corresponding to an orthogonal basis or a tight frame.The most tested and used dictionaries in the inventors' study ofresistivity images are the wavelet and curvelet. The curvelet seems tooutperform the wavelet for resistivity images, and hence the inventorsdecided to concentrate on the curvelet dictionary for an initialevaluation of the in-painting process.

The good performance of the curvelet versus wavelet dictionary issupported by the fact that most of the morphological components inresistivity images are curves (often sinusoids) related to bedding andfractures. While wavelets are certainly suitable for objects where theinteresting phenomena, e.g. singularities, are associated withexceptional points, they appear ill-suited for detecting, organizing, orproviding a compact representation of intermediate dimensionalstructures.

In general, curvelets are more appropriate tools in the case ofresistivity image logs because they efficiently address very importantproblems where wavelet ideas are far from ideal—such as optimally sparserepresentation of objects with edges. Curvelets provide optimally sparserepresentations of objects which display curve-punctuated smoothnessexcept for discontinuity along a general curve with bounded curvature.Such representations are nearly as sparse as if the object were notsingular, and turn out to be far sparser than the wavelet decompositionof the object. The curvelet dictionary is also useful for optimalresistivity image reconstruction in severely ill-posed conditions(missing data). Curvelets also have special micro-local features whichmake them especially adapted to reconstruction problems with missingdata and also from noisy and incomplete data (where some pads are notworking properly for example).

Despite these reservations in the inventors' initial work, the inventionis applicable in the case of using wavelets, or other representations aslisted.

Resistivity images can contain both geometry and texture, so they demandapproaches that work for images containing both cartoon and texturelayers. The concept of MCA additively decomposing the image into layersis preferred, allowing a combination of layer-specific methods forfilling in. In this way, the in-painting is done separately in eachlayer, and the completed layers are superposed to form the output image.

The MCA approach is based on optimising the sparsity of each layer'srepresentation. The central idea is to use a set of dictionaries(wavelet, curvelet, or one of the other representations indicated), eachone adapted to represent a specific feature. The dictionaries aremutually incoherent; each leads to sparse representations for itsintended content type, while yielding non-sparse representations on theother content type.

The basis pursuit de-noising (BPDN) algorithm is relied upon for properseparation, as it seeks the combined sparsest solution, which shouldagree with the sparse representation of each layer separately. The BPDNalgorithm was shown to perform well when constrained by total-variation(TV) regularization.

Overall the method and apparatus of the invention, regardless of theexact MCA method steps employed, permit significant improvements in thequality of image logs, and in particular resistivity image logs, for thereasons set out herein.

Resistivity Image Decomposition Using the MCA Approach

Consider the input image constructed from the measurement of theresistivity from the whole pads and the whole buttons, containing Ntotal pixels, be represented as a 1D vector of length N by lexicographicordering. To model images Y_(n) containing different geometricalstructure, we assume that a matrix A_(n)∈M^(N×L) (where typically L>>N)allows sparse decomposition, written informally asY_(n)=A_(n)x_(n),  (1)where x_(n) is sparse dictionary.

Here sparsity can be quantified by any of several different quasi-normsincluding the l_(o) norm, which is equivalent to the number of non-zerocomponents in the vector x and l_(p)-norms ∥x∥_(p)=(Σ|x(i)|^(p))^(1/p)with p<1, with small values of any of these indicating sparsity.Sparsity measured in the l_(o) norm implies that the texture image canbe a linear combination of relatively few columns from A_(n).

There are two more technical assumptions. First, localisation: therepresentation matrix A_(n) is such that if the geometrical structure(cartoons) appears in parts of the image and is otherwise zero therepresentation is still sparse, implying that this dictionary employs amulti-scale and local analysis of the image content.

Second, incoherence: A_(n) should not, for example, be able to representtexture images sparsely. We require that when Y_(n)=A_(n)x_(n) isapplied to images containing texture content, the resultingrepresentations are non-sparse. Thus, the dictionary A_(n) plays a roleof a discriminant between content types, preferring cartoon content.

If we want to consider, for example, the texture layer, then anotherappropriate dictionary should be used where, in contrast to the above, acartoon image is non sparsely represented by the new dictionary. Thisleads to a general case of decomposing the image in a multipledictionary where the sparsity is specific for each content type.

Considering only one dictionary at time, and if we work with the l_(o)norm as a definition of sparsity, we need to solve the followingobjective function:

$\begin{matrix}{\left\{ {\underset{\_}{x}}_{n}^{opt} \right\} = {{\underset{\{{\underset{\_}{x}}_{n,}\}}{argmin}{{\underset{\_}{x}}_{n}}_{0}\mspace{14mu}{s.t.\mspace{14mu}\underset{\_}{Y}}} = \underset{\_}{A_{n}x_{n}}}} & (2)\end{matrix}$

This optimisation formulation should lead to a successful separation ofthe image content A_(n) x _(n) specific to the geometrical structure(cartoon), for example. This expectation relies on the assumptions madeearlier about A_(n) being able to sparsely represent one content typewhile being highly non-effective in sparsifying the other.

The formulated problem in Equation (2) is non-convex and seeminglyintractable. Its complexity grows exponentially with the number ofcolumns in the overall dictionary. The basis pursuit (BP) methodsuggests the replacement of the l_(n)-norm with an l₁-norm, thus leadingto a tractable convex optimization problem, in fact being reducible tolinear programming:

$\begin{matrix}{\left\{ {\underset{\_}{x}}_{n}^{opt} \right\} = {{\underset{\{{\underset{\_}{x}}_{n,}\}}{argmin}{{\underset{\_}{x}}_{n}}_{1}\mspace{14mu}{s.t.\mspace{14mu}\underset{\_}{Y}}} = \underset{\_}{A_{n}x_{n}}}} & (3)\end{matrix}$

For certain dictionaries and for objects that have sufficiently sparsesolutions, the BP approach can actually produce the sparsest of allrepresentations.

If the image is noisy it cannot be cleanly decomposed into sparsecartoon layers. Therefore a noise-cognizant version of BP can be used:

$\begin{matrix}{\left\{ {{\underset{\_}{x}}_{n}^{opt},} \right\} = {{\underset{\{{\underset{\_}{x}}_{n,}\}}{argmin}{{\underset{\_}{x}}_{n}}_{1}\mspace{14mu}{s.t.\mspace{11mu}{\;{\underset{\_}{Y} - {A_{n}{\underset{\_}{x}}_{n}}}}_{2}}} < ɛ}} & (4)\end{matrix}$

The decomposition of the image in that case is only approximate, leavingsome error to be absorbed by content that is not represented well by theappropriate dictionary. The parameter ε stands for the noise level inthe image.

Alternatively, the constrained optimization in Equation (4) can bereplaced by an unconstrained penalized optimization. Bothnoise-cognizant approaches have been analyzed theoretically, providingconditions for a sparse representation to be recovered accurately.

Also useful in the context of sparsity-based separation is theimposition of a total variation (TV) penalty. This performs particularlywell in recovering piecewise smooth objects with pronounced edges—i.e.,when applied to the curve (sinusoid) layer. It is most convenientlyimposed as a penalty in an unconstrained optimization:

$\begin{matrix}{\left\{ {\underset{\_}{x}}_{n}^{opt} \right\} = {{\underset{\{{\underset{\_}{x}}_{n,}\}}{argmin}{{\underset{\_}{x}}_{n}}_{1}} + {\lambda{\;{\underset{\_}{Y} - {A_{n}{\underset{\_}{x}}_{n}}}}_{2}^{2}} + {\gamma\;{TV}\left\{ {A_{n}{\underset{\_}{x}}_{n}} \right\}}}} & (5)\end{matrix}$where the total variation of an image I, TV(I) is essentially thel₁-norm of the gradient. Penalising with TV forces the image A_(n) x_(n) to have a sparser gradient, and hence to be closer to a piecewisesmooth image.

Note that A_(n), should be a known transform. For texture content onemay use transforms such as local Discrete Cosine Transform DCT, Gabor orwavelet packets (that typically are oscillatory ones to fit texturebehaviour). For the cartoon content one can use wavelets, curvelets,ridgelets, or contourlets, and there are several more options. In bothcases, the proper choice of dictionaries depends on the actual contentof the image to be treated or even a combined version of the abovedictionaries when necessary. The best choice of the curvelet transformfor in-filling the gaps between pads depends on a priori knowledge ofthe resistivity images and on some experience conducted on differentreal data recorded from different wells. This choice made may vary forother images with other contexts (an example being sonic images).

Resistivity Image In-painting Using MCA

Assume that the missing pixels between pads are indicated by a ‘mask’matrix M∈M^(N×L). The main diagonal of M encodes the pixel status,namely ‘1’ for an existing pixel and ‘0’ for a missing one. Thus, in theequation (5) we can incorporate this mask by

$\begin{matrix}{\left\{ {\underset{\_}{x}}_{n}^{opt} \right\} = {{\underset{\{{\underset{\_}{x}}_{n,}\}}{argmin}{{\underset{\_}{x}}_{n}}_{1}} + {\lambda{\;{\underset{\_}{M\left( Y \right.} - {A_{n}{\underset{\_}{x}}_{n}}}}_{2}^{2}} + {\gamma\;{TV}\left\{ {A_{n}{\underset{\_}{x}}_{n}} \right\}}}} & (6)\end{matrix}$

Doing this, one desires an approximate decomposition of the input imageX to cartoon parts A_(n) x _(n), and the fidelity of the representationis measured with respect to the existing measurements only, disregardingmissing pixels. The idea is that once A_(n) x _(n) are recovered, thoserepresent entire images, where the missing data in the gaps are filledin by the dictionary basis function.

-   -   The total-variation penalty in Equation (6) suppresses the        typical ringing artefacts encountered in using linear        transforms. This can be crucial near sharp edges, where ringing        artefacts are strongly visible.    -   The above models (6) consider the image as a whole and are not        based on local information only. Thus, multi-scale relations        that exist in the image that could be exploited are overlooked.

Overall, the method and apparatus of the invention, regardless of theexact MCA method steps employed, permit significant improvements in thequality of image logs, and in particular resistivity image logs, for thereasons set out herein.

The listing or discussion of an apparently prior-published document inthis specification should not necessarily be taken as an acknowledgementthat the document is part of the state of the art or is common generalknowledge.

What is claimed is:
 1. A method of image processing implemented with oneor more processing devices, the method comprising: obtaining, with theone or more processing devices, image information derived fromgeological log data signals generated through use of a logging toolhaving one or more electrodes interacting with a formation intersectedby a borehole; constructing, with the one or more processing devices,missing image information missing from the obtained image informationdue to destroyed or occluded parts of the obtained image information byusing cues from observed data comprising the steps of: in respect of oneor more data dimensions associated with missing values in a log dataset, decomposing the log data signal into a plurality of morphologicalcomponents, and morphologically reconstructing the log data signal suchthat missing values are estimated; and producing, with the one or moreprocessing devices, a resulting image incorporating the missing imageinformation into the obtained image information.
 2. The method of claim1, comprising performing the steps of decomposing and morphologicallyreconstructing in respect of all the missing information in the dataset.
 3. The method of claim 1, wherein the decomposition includes use ofa dictionary of elemental bases including one or more selected from thelist including discrete cosine transforms, wavelet transforms, waveletpacket transforms, ridgelet transforms, curvelet transforms, andcontourlet transforms.
 4. The method of claim 1, comprising the step ofperforming one or more automatic feature recognition and/or machineinterpretation steps following the step of morphologicallyreconstructing.
 5. The method of claim 4, wherein at least one saidautomatic feature recognition and/or machine interpretation stepcomprises one or more of an edge recognition step and/or a texturerecognition step.
 6. The method of claim 1, comprising the step ofseparating each elemental signal base into a plurality of respectivemorphological components on the basis of an assumption that in order foreach elemental signal base to be separated there exists a dictionary ofelemental bases enabling its construction using a sparse representation.7. The method of claim 6, further comprising the steps of: assuming thateach respective morphological component is sparsely represented in aspecific transform domain; and amalgamating each transform attached to arespective morphological component into a dictionary.
 8. The method ofclaim 7, comprising the step of identifying the sparsest representationof morphological components and using the thus-identified components tode-couple the components of the signal content.
 9. The method of claim8, comprising using a basis pursuit (BP) algorithm to carry out the stepof identifying.
 10. The method of claim 1, wherein the morphologicalcomponents comprises texture and piece-wise parts.
 11. The method ofclaim 10, wherein the piece-wise parts comprise image content; andwherein the step of decomposing comprises decomposing the image parts inelemental contents; and wherein the method comprises separatelyconstructing information missing from the elemental contents, beforeperforming the step of morphologically reconstructing.
 12. The method ofclaim 11, wherein the geological log data signals are measures offormation resistivity in the form of an image containing N pixels andwherein the method includes representing the geological log data signalsas a one-dimensional vector, of length N, by lexicographic ordering. 13.The method of claim 12, wherein the step of decomposing comprisesrepresenting the image content by a dictionary: A_(n∈M) ^(N×L) wherein apursuit algorithm is such that the image content is sparsely representedin dictionary A_(n.)
 14. The method of claim 13, wherein sparsity isquantified by one of a plurality of quasi-norms.
 15. The method of claim14, wherein the quasi-norm is the l₀ norm, which is equivalent to thenumber of non-zero components in the vector x and l_(p)-norms∥x∥_(p=(Σ|x(i)|) ^(p))^(1/p) with p<1, and in which small values of anyof these indicate sparsity.
 16. The method of claim 15, wherein thepursuit algorithm seeks to solve$\left\{ {\underset{\_}{x}}_{n}^{opt} \right\} = {{\underset{\{{\underset{\_}{x}}_{n}\}}{argmin}{{\underset{\_}{x}}_{n}}_{0}\mspace{14mu}{s.t.\mspace{14mu}\underset{\_}{Y}}} = {A_{n}{\underset{\_}{x}}_{n}}}$with the result that A_(n) x _(n) contains the image content.
 17. Themethod of claim 14, wherein the quasi-norm is the l₁, norm, and whereinthe pursuit algorithm seeks to solve$\left\{ {\underset{\_}{x}}_{n}^{opt} \right\} = {{\underset{\{{\underset{\_}{x}}_{n}\}}{argmin}{{\underset{\_}{x}}_{n}}_{1}\mspace{14mu}{s.t.\mspace{14mu}\underset{\_}{Y}}} = {A_{n}{\underset{\_}{x}}_{n}}}$with the result that A_(n) x _(n) contains the image content.
 18. Themethod of claim 17, wherein the pursuit algorithm is a basis pursuit(BP) that solves the expression using linear programming.
 19. The methodof claim 17, wherein the pursuit algorithm seeks to solve$\left\{ {\underset{\_}{x}}_{n}^{opt} \right\} = {{\underset{\{{\underset{\_}{x}}_{n}\}}{argmin}{{\underset{\_}{x}}_{n}}_{1}\mspace{14mu}{s.t.\mspace{11mu}{\;{\underset{\_}{Y} - {A_{n}{\underset{\_}{x}}_{n}}}}_{2}}} < ɛ}$in which ε is a parameter corresponding to the level of noise in theimage log Y, with the result that A_(n) x _(n) contains the imagecontent.
 20. The method of claim 17, wherein the pursuit algorithm seeksto solve$\left\{ {\underset{\_}{x}}_{n}^{opt} \right\} = {{\underset{\{{\underset{\_}{x}}_{n,}\}}{argmin}{{\underset{\_}{x}}_{n}}_{1}} + {\lambda{\;{\underset{\_}{Y} - {A_{n}{\underset{\_}{x}}_{n}}}}_{2}^{2}} + {\gamma\;{TV}\left\{ {A_{n}{\underset{\_}{x}}_{n}} \right\}}}$in which TV represents a total variation penalty and the parameter λ>0is a scalar representation parameter and the total variation penaltyincreases the sparseness gradient of A_(n) x _(n), with the result thatA_(n) x _(n) contains the image content.
 21. The method of claim 12,further comprising compensating for at least one variation in one ormore environmental factors that are variable depending on theenvironment to which the geological log data signals pertain by assumingthat pixels of an image log corresponding to missing log data areindicated by a mask matrix M∈M^(N×L) the main diagonal M of whichencodes the pixel status as 1 in the case of an existing pixel and 0 isthe case of missing data and wherein the pursuit algorithm seeks tosolve$\left\{ {\underset{\_}{x}}_{n}^{opt} \right\} = {{\underset{\{{\underset{\_}{x}}_{n}\}}{argmin}{{\underset{\_}{x}}_{n}}_{1}} + {\lambda{\;{\underset{\_}{M\left( Y \right.} - {A_{n}{\underset{\_}{x}}_{n}}}}_{2}^{2}} + {\gamma\;{TV}\left\{ {A_{n}{\underset{\_}{x}}_{n}} \right\}}}$with the result that A_(n) x _(n) contains the image content.
 22. Themethod of claim 1, wherein obtaining, with the one or more processingdevices, the geological log data signals generated through use of thelogging tool having the one or more electrodes interacting with theformation intersected by the borehole comprises logging the formation byoperating the logging tool in the borehole to interact the one or moreelectrodes with the formation.
 23. A resistivity image logging toolhaving operatively connected or connectable thereto one or moreprocessing devices for carrying out, on data signals generated by thetool, a method according to claim 1.